In the QCD sum rules for the traditional mesons, we always introduce a parameter \(\kappa \)  to parameterize the deviation from the factorization hypothesis by hand, for example, in the case of the four quark condensate, \(\langle \bar{q}q\rangle ^2 \rightarrow \kappa \langle \bar{q}q\rangle ^2\)  [1]}, [2]}, [3]}. As the \(\langle \bar{q}q\rangle ^2\)  is always companied with the fine-structure constant \(\alpha _s=\frac{g_s^2}{4\pi }\) , and plays a minor important role,
the deviation from \(\kappa =1\) , for example, \(\kappa =2\sim 3\) , cannot make much difference, though the value \(\kappa >1\)  can lead to better QCD sum rules in some cases.
In fact, the vacuum saturation works well in the large \(N_c\)  limit [4]}.
